Approximate Counting of Matchings in Sparse Hypergraphs
نویسندگان
چکیده
In this paper we give a fully polynomial randomized approximation scheme (FPRAS) for the number of all matchings in hypergraphs belonging to a class of sparse, uniform hypergraphs. Our method is based on a generalization of the canonical path method to the case of uniform hypergraphs.
منابع مشابه
Approximate Counting of Matchings in Sparse Uniform Hypergraphs
In this paper we give a fully polynomial randomized approximation scheme (FPRAS) for the number of matchings in k-uniform hypergraphs whose intersection graphs contain few claws. Our method gives a generalization of the canonical path method of Jerrum and Sinclair to hypergraphs satisfying a local restriction. Our proof method depends on an application of the Euler tour technique for the canoni...
متن کاملApproximate Counting of Matchings in (3, 3)-Hypergraphs
We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as (3, 3)hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite (3, 3)-hypergraphs. The proof tech...
متن کاملCounting Hypergraph Matchings up to Uniqueness Threshold
We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter λ, each matching M is assigned a weight λ|M |. The counting problem is formulated as computing a partition function that gives the sum of the weights of all matchings in a hypergraph. This problem unifies two extensively studied statistical...
متن کاملComputing the Partition Function for Perfect Matchings in a Hypergraph
Given non-negative weights wS on the k-subsets S of a km-element set V , we consider the sum of the products wS1 · · ·wSm over all partitions V = S1 ∪ . . . ∪ Sm into pairwise disjoint k-subsets Si. When the weights wS are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor. ...
متن کاملA counting lemma for sparse pseudorandom hypergraphs
Our main result tells us that mild density and pseudorandom conditions allow one to prove certain counting lemmas for a restricted class of subhypergraphs in a sparse setting. As an application, we present a variant of a universality result of Rödl for sparse, 3-uniform hypergraphs contained in strongly pseudorandom hypergraphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1202.5885 شماره
صفحات -
تاریخ انتشار 2012